An algebraic approach to the Hubbard model

TL;DR

This paper explores the algebraic structure of an integrable Hubbard-Shastry lattice model linked to superalgebra symmetries, revealing connections to Yangian symmetries and the algebraic interpretation of the Hubbard Hamiltonian.

Contribution

It provides an algebraic framework for the Hubbard model, connecting Yangian symmetries and secret symmetries to integrable lattice models based on superalgebra structures.

Findings

Yangian symmetries of the R-matrix relate to the Hubbard model's Yangian symmetry.

Hubbard Hamiltonian has an algebraic interpretation as the secret symmetry.

The algebraic structure encompasses models related to AdS/CFT and Shastry's R-matrix.

Abstract

We study the algebraic structure of an integrable Hubbard-Shastry type lattice model associated with the centrally extended su(2|2) superalgebra. This superalgebra underlies Beisert's AdS/CFT worldsheet R-matrix and Shastry's R-matrix. The considered model specializes to the one-dimensional Hubbard model in a certain limit. We demonstrate that Yangian symmetries of the R-matrix specialize to the Yangian symmetry of the Hubbard model found by Korepin and Uglov. Moreover, we show that the Hubbard model Hamiltonian has an algebraic interpretation as the so-called secret symmetry. We also discuss Yangian symmetries of the A and B models introduced by Frolov and Quinn.